Analysis of the onset of buoyancy-driven convection in a water layer formed by ice melting from below

Kim, Min Chan; Choi, Chi Kyu; Yoon, Do‐Young

doi:10.1016/j.ijheatmasstransfer.2008.04.006

Cited by 17 publications

(4 citation statements)

References 22 publications

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“…The critical Rayleigh number, which is defined as the Rayleigh number when natural convection occurs in the liquid phase (black circles in Fig.5), tends to decrease with increasing heat flux when IPF is the same. Yen (1968) and Kim et al (2008) showed that the critical Rayleigh number increased as the temperature difference between bulk fluid and heater increased when the ice in the cavity was heated from below. In this study, the temperature difference between heater and bulk fluid increased when the heat flux increased but the critical Rayleigh number decreased.…”

Section: Methodsmentioning

confidence: 99%

“…Fukusako et al (1977) reviewed the melting heat transfer in a rectangular cavity filled with ice heated from below. Yen (1968) and Kim et al (2008) suggested that the onset of natural convection in liquid phase is affected by the temperature difference between the heater and the melting surface. Fukusako et al (1977) reorganized Yen's data and showed that the critical Rayleigh number increases with increasing temperature of the heater.…”

Section: Introductionmentioning

confidence: 99%

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Melting heat transfer in rectangular cavity filled with ice slurry heated from below

Miyagawa

Okabe

Miyanishi

et al. 2019

JFST

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Ice slurry is a homogeneous mixture of small ice particles and a carrier liquid. It is widely used in many fields. Previous studies have gradually clarified its heat transfer in high ice packing factor (IPF). However, only a few studies have focused on the mechanism of heat transfer with low IPF in a cavity heated from below. The objective of this study is to experimentally clarify the melting heat transfer of ice slurry in a cavity heated from below with low IPF to develop a direct contact medical cooling system. To observe the melting behavior of ice slurry, the test section was made of acrylic resin (100 mm × 60 mm× 30 mm) and a silicone rubber heater that was used for heating under constant heat flux conditions. We measured the surface temperature of the heater and the liquid thickness. We showed that the melting process can be divided into three stages. In the first stage, heat conduction dominated the process of heat transfer and the temperature of the heater rapidly increased. In the second stage, natural convection heat transfer dominated the process of heat transfer that increased the melting rate of ice slurry and decreased the temperature of the heater. In the third stage, heat conduction dominated the process of heat transfer in the concentration stratification. This led to a decrease in the melting rate and an increase in the temperature of the heater. Our result also showed that the melting process of the ice slurry is slow enough to consider it the quasi-steady state in the range of 10 4 < Ra * < 10 7 as compared to the development of the velocity and temperature fields.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Melting heat transfer in rectangular cavity filled with ice slurry heated from below

Miyagawa

Okabe

Miyanishi

et al. 2019

JFST

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“…In the current study, behavior of the temperature and velocity of fluid flowing inside the closed cavities with different boundary conditions is considered. The literature explains a vivid usage of the natural convection flow within the closed entities because of its practical relevance in various applications, such as heat exchangers [1] and [2], room heating and ventilation design [3][4][5], melting [6], etc., Different shapes of cavities, circle [7], trapezoid [8], square [9] and [10], triangle [11][12][13] has been grabbing the attention of researchers since decades. The non-dimensional governing equations of the 2D flow problem is formulated with the penalty finite element method.…”

Section: Introductionmentioning

confidence: 99%

Study of fluid flow inside closed cavities using computational numerical methods

Prabhakar

2021

Int. J. Simul. Multidisci. Des. Optim.

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The temperature distribution and distortion of fluid flow inside the closed cavities, square and triangle, are studied for different boundary conditions. Two different conditions of thermal boundary conditions are used for studying square cavities: (i) Left wall is hot, right wall is cold, top and bottom walls are adiabatic. (ii) Left and right walls are cold, top wall is adiabatic, bottom wall is hot. For triangular enclosure, the boundary conditions are (i) the vertical wall is insulated, bottom wall is hot. (ii) The vertical wall is hot, the bottom wall insulated and the inclined walls are kept cold in both conditions. The velocity of the flow is observed by means of stream function and the temperature distribution is displayed in the form of contours. The study is carried out in ANSYS software. The mathematical procedure for solving the nonlinear system of partial differential equations by penalty finite element method involving bi-quadratic elements is also discussed in detail.

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“…Although this analogy breaks down when disturbances enter the nonlinear regime, we nevertheless expected much of the qualitative nature of the unsteady problem of Selim and Rees (2007a) to carry over to the present configuration. The study of the stability of such nonsimilar boundary layers is one where there remains much interest and activity, some examples of which are the recent articles by Ennis-King et al (2005) on anisotropic media, Kim et al (2008) on the melting of ice within a porous medium, Riaz et al (2006) who also present some detailed nonlinear simulations and Nouri-Borujerdi et al (2007) on the effects of local thermal non-equilibrium. However, there remains some differences of opinion in the literature about the best way of defining instability.…”

Section: Introductionmentioning

confidence: 99%

The Onset and Nonlinear Development of Vortex Instabilities in a Horizontal Forced Convection Boundary Layer With Uniform Surface Suction

Rees

2008

Transp Porous Med

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We consider the flow and heat transfer caused by a strong external flow passing over a hot surface with uniform surface suction. When the Péclet number based on the external velocity is sufficiently large, the resulting thermal boundary layer develops in a nonsimilar manner until it attains an asymptotic state which is independent of the streamwise coordinate, x, when it is dominated by the surface suction. For sufficiently large, but moderate, values of the Darcy-Rayleigh number this boundary layer becomes unstable to streamwise vortex disturbances. We employ a parabolic solver to determine how such disturbances, when placed very close to the leading edge, evolve with distance downstream. Neutral stability is then defined to be when a suitable energy functional ceases to decay/grow as x increases. Thus a neutral curve may be mapped out based upon the behaviour of this functional. Given that the uniform asymptotic state is well known to admit subcritical instabilities, our linearised analysis is extended into the nonlinear domain and the effect of different magnitudes of disturbance is ascertained. It is found that a surprisingly rich variety of vortex pattern emerges which is sometimes sensitively dependent on the values of the governing parameters. These patterns include wavy vortices and abrupt changes in perceived wavelength.

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Analysis of the onset of buoyancy-driven convection in a water layer formed by ice melting from below

Cited by 17 publications

References 22 publications

Melting heat transfer in rectangular cavity filled with ice slurry heated from below

Melting heat transfer in rectangular cavity filled with ice slurry heated from below

Study of fluid flow inside closed cavities using computational numerical methods

The Onset and Nonlinear Development of Vortex Instabilities in a Horizontal Forced Convection Boundary Layer With Uniform Surface Suction

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